According to the document:
In contrast to
any data stored in the Tangle, the communication layer, therefore, does not
necessarily require the use of post-quantum cryptography right now, but it can
be swapped when quantum attacks become more imminent in the future.
In case of quantum computer attacks become feasible, a dishonest node that has the power to partition the network, could double spend and sign different, conflicting messages "from" many nodes to different other nodes (in the two partitions of the network), therefore making part of the network to reject a transaction that is accepted in the other part.
However, when the networks rejoin, it will still eventually result in a consensus that both double spends are invalid. Perhaps one of the receivers has already believed before that his transaction was legitimately accepted (because the nodes believed that) and already sent his valuable goods to the attacker.
I think the whitepaper promotes the idea that it will swap this consensus signing algorithm with a quantum-resistant one once quantum attacks get more feasible and, therefore, quantum resistant cryptography gets better. Unlike the signatures used by your IOTA addresses, such an algorithm switch has no impact on your balance and you don't have to transition your money. The signatures are only used for the consensus protocol.